Computational Methods in Engineering

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Articulated liquid cargo vehicles transporting inflammable fuels and dangerous chemical products require special consideration when traveling on urban roads or cruising at highway speeds. The road safety and handling of these kinds of vehicles may be adversely affected when negotiating sharp turns or travelling on slippery roads, which may result in either lateral instabilities or complete rollover of these tanker vehicles. Moreover, directional instabilities in these kinds of vehicle may also introduce an excessive yaw swing or may initiate the jack- knifing of the articulated tanker trucks. In order to overcome the instabilities of these tanker vehicles, installation of lateral baffles in the form of separating walls in the tanker were considered. The static roll and yaw plane models of these vehicles including lateral translation of the liquid inside the tank were developed. Using the static roll model, the rollover threshold of the vehicle is analyzed and the effect of these separating walls on the stability of the vehicle is studied. The yaw plane model is then used to predict the transient response and stability of the tanker vehicle under various road maneuvers. The governing differential equations were solved numerically to obtain the simulation results and optimum values of the parameters. Keywords: Tanker, Vehicle, Stability, vehicle dynamic, rollover, lateral baffles

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Finding the collapse susceptible portion of a power system is one of the purposes of voltage stability analysis. This part which is a voltage control area is called the voltage weak area. Determining the weak area and adjecent voltage control areas has special importance in the improvement of voltage stability. Designing an on-line corrective control requires the voltage weak area to be determined by a sufficiently rapid and precise method. In this paper, a new algorithm based on assigning a vector to each power system bus is presented. These vectors indicate buses conditions from the viewpoint of voltage stability. In this new method, using the clustering methods such as kohonen neural network, fuzzy C-Means algorithm and fuzzy kohonen algorithm, voltage control areas are determined The proposed method has advantages such as determining PV and PQ buses which belong to the weak area simultanously, under all operating conditions and without a need to system model. Also by comparing the results of applying clustering methods, it has been observed that, due to simplicity of implementation and precision of the results, the two dimensional kohonen neural network is a more suitable tool for clustering power system to voltage control areas than the fuzzy C-Means and fuzzy kohonen methods. Keywords: Voltage stability, Voltage weak area, Voltage control area, Corrective control, Pattern recognition, Kohonen neural network, Fuzzy C-Means algorithm, Fuzzy Kohonen algorithm.

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In a de-regulated open access environment, reactive power is one of the ancillary services which must be provided by an Independent System Operator (ISO). In this paper, a new algorithm is proposed in which reactive power resources are initially so tuned that optimum security in terms of voltage profile and voltage stability are achieved while at the same time, the system losses are minimized. The resulting optimization case is solved as an Extended Multi-objective Optimal Power Flow (EMOPF) problem using Lexico Graphic Method (LGM). Thereafter, using the concept of Fair Resource Allocation (FRA), the reactive powers generated are distributed among existing transactions so that the costs incurred are properly and fairly recovered. The algorithm is successfully tested on a typical power system. Keywords: Reactive Power, Reactive Power Management, Reactive Power Pricing, Voltage Profile, Voltage Stability, Deregulated Environment, Open Access

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In this paper, dynamic and stability analysis of a flexible cam-follower system is investigated. Equation of motion is derived considering flexibility of the follower and camshaft. Viscous and Coulomb frictions are considered in the rocker arm pivot. The normalized equation of motion of the system is a 2nd- order differential equation with periodic coefficients. Floquet theory is employed to study parametric stability of the system. Stability diagrams are presented and the effects of varying cam profiles and motion events on the stability of the system are compared. Results show that viscous and Coulomb frictions stabilize the motion of the system

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Methods for calculating Available Transfer Capability (ATC) of the transmission systems may be grouped under Static and Dynamic methods. This paper presents a fast dynamic method for ATC calculations, which considers both Transient Stability Limits and Voltage Stability Limits as terminating criteria. A variation of Energy Function Method is used to determine the transient stability limit and the determinant of the Jacobian matrix of the system is used as an index to determine the voltage stability limit. A novel method is used to approximately calculate this determinant. Combining these two methods, an algorithm that calculates ATC, based on both voltage and angle dynamic stability is presented. The advantage of this algorithm, besides considering both voltage and angle dynamic stability, is its high speed. This speed of calculation makes the algorithm a perfect candidate to be used in screening contingencies and to determine those cases that need to be further analyzed. To demonstrate the validity, efficiency, and the speed of the new method, it is employed in the calculation of ATC for numerical examples with 2, 3, 7 (CIGREE), 10, 30 (IEEE) and 145 (Iowa State) buses.

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Neutral stability limits for wake flow behind a flat plate is studied using spectral method. First, Orr-Sommerfeld equation was changed to matrix form, covering the whole domain of solution. Next, each term of matrix was expanded using Chebyshev expansion series, a series very much equivalent to the Fourier cosine series. A group of functions and conditions are applied to start and end points in the mathematical domain of the solution so as to avoid error accomulation at these points. The scheme ends with two matrices which result from the Orr-Sommerfeld equation. These matrices are solved, in conjunction, with boundary conditions ending up with a curve of neutral points of stability for an assumed velocity profile. Results are compared with other existing numerical methods and experiments, and the accuracy of the method is confirmed.

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Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange interpolation functions. The spectral method is, in fact, the solution of motion equation for an axially moving plate. Although this method has some limitations concerning boundary condition of plate and in-plane forces, it leads to an exact solution of free vibration and stability of plates travelling on parallel rollers. The method can be used as a benchmark of accuracy of other numerical methods.

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Considering the vulnerability of double-layer grid space structures to progressive collapse phenomenon, it is necessary to pay special attention to this phenomenon in the design process. Alternate path method is one of the most appropriate and accepted methods for progressive collapse resistant design of structures. Alternate Path Method permits local failure to occur but provides alternate paths around the damaged area so that the structure is able to absorb the applied loads without overall collapse. Following the sudden initial local failure event, severe dynamic effects may arise which should be taken into account in determining the realistic collapse behavior of the structure. In this paper, a new methodology based on alternate path method is presented to apply dynamic effects of initial local failure. The method is called nonlinear dynamic alternate path method. Due to its capability to take account of dynamic nature of the failure, this method can be used to evaluate realistic collapse behavior of the structure and to investigate the vulnerability of the structure to progressive collapse phenomenon.

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In this paper, the equation of motion of an elastic 2 DoF wing model has been derived using Lagranges method. The aerodynamic loads on the wing were calculated via the Strip-Theory and the effect of compressibility was included. Wing deflections due to bending and twist motions were determined using the Assume-Mode method. The aeroelastic equations were solved numerically using the V-g method. The results obtained for different types of wings were in good agreement with experimental data.

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In this paper, considering all the linear and nonlinear inertia terms of moving masses on a flexible beam, the dynamic response and dynamic stability of the beam are studied. Homotopy perturbation method is used to perform the analysis and results are provided in a stability map for the different values of mass and velocity of the moving masses. It is concluded that there is a borderline in the diagram that separates the stable and unstable regions. For the first time, this borderline is determined semi-analytically. Results of the stability analysis are validated using the Floquet theory. In addition to this borderline, it is also concluded that the Homotopy perturbation method is capable of evaluating the new critical values for mass and velocity which cause vibration resonance in the beam. The locus of these resonant points, which is totally a new finding in dynamic analysis of beam-moving mass problem, is determined semi-analytically. Finally, the effect of the friction between the beam and the moving mass is studied on the stability of the system and resonant conditions. Accuracy of the results for this case is also evaluated with a numerical simulation.

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For solving the dynamic equilibrium equation of structures, several second-order numerical methods have so far
been proposed. In these algorithms, conditional stability, period elongation, amplitude error, appearance of spurious frequencies
and dependency of the algorithms to the time steps are the crucial problems. Among the numerical methods, Newmark average
acceleration algorithm, regardless of existence of spurious frequencies, is very popular in the structural dynamics due to its
unconditionally stability status of the method. Recently, several first-order methods have been introduced for resolving the
accuracy and stability issues. However, in these methods stability, accuracy and error in inversion of the state matrix are known
as major issues. When the state matrix became singular or ill conditioned, numerical errors will occure in the computational
process. Many of the available first-order methods were to improve the stability and accuracy and also to remove the error of
inversion. Even though the introduced methods are conditionally stable, no investigation on errors, occuring during dynamic
loading, has been reported for them. The main purpose of this paper is to utilize a specific decomposition method based on
Singular Value Decomposition (SVD) for modifying PIM algorithm. Using the SVD inversion technique, the singularity problem
of the state matrix has been resolved. In this paper, the modified method is called PIMS. As well, by applying the developed
method for dynamic loading, the error of responses has been investigated. The results show that PIMS algorithm is stable and,
comparing with secoend order Newmark and other available first order methods, has more accuracy.

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In this paper, a new method is proposed for fuzzy structural reliability analysis; it considers epistemic uncertainty arising from the statistical ambiguity of random variables. The proposed method, namely, fuzzy dynamic-directional stability transformation method, includes two iterative loops. An internal algorithm performs the reliability analysis using the dynamic-directional stability transformation method and an external algorithm performs the fuzzy analysis by applying the alpha-cut level optimization method based on the genetic algorithm. Implementation of the proposed method, which solves some nonlinear performance functions, indicates the efficiency and robustness of the dynamic-directional stability transformation method, as compared to other first order reliability methods.

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Graphene is one of the nanostructured materials that has recently attracted the attention of many researchers. This is due to the increasing expansion of nanotechnology and the application of this nanostructure in technology and industry owing to its mechanical, electrical and thermal properties. Thermal buckling behavior of single-layered graphene sheets is studied in this paper. Given the failure of classical theories to consider the scale effects and the limitations of the nano-sized experimental investigations of nano-materials, the small-scale effect is taken into account in this study, by employing the modified couple stress theory which has only one scale parameter. On the other hand, the two-variable refined plate theory, which considers the shear deformations in addition to bending deformations, is used to define the displacement field and to formulate the problem. The developed finite strip method formulation is used to evaluate the critical buckling temperature of the nanoplates. The validity of the proposed method is confirmed by comparing the results of this study with the those in the literature. The effects of different boundary conditions, temperature changing patterns, aspect ratio, and the ratio of length parameter to thickness on the critical buckling temperature are considered and the results are presented in the form of Tables and Figures

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In this paper, dynamic instability due to parametric and external resonances of moderately thick functionally graded rectangular plates, under successive moving masses, is examined. Plate mass per unit volume and Young’s modulus are assumed to vary continuously through the thickness of the plate and obey a power-law distribution of the volume fraction of the constituent. The considered rectangular plates have two opposite simply supported edges while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The governing coupled partial differential equations of the plate are derived based on the first-order shear deformation theory with consideration of the rotational inertial effects and the transverse shear stresses. All inertial components of the moving masses are considered in the dynamic formulation. Using the Galerkin procedure, the partial differential equations are transformed into a set of ordinary differential equations with time-dependent coefficients. The Homotopy Analysis Method (HAM) is implemented as a semi-analytical method to obtain stable and unstable zones and external resonance curves in a parameters space. The effects of the index of volume fraction, thickness to length ratio, and different combinations of the boundary conditions on the dynamic stability of the system are also investigated. The results indicate that decreasing the index of volume fraction, increasing thickness to length ratio, and higher degree of edge constraints (respectively from free to simply-supported to clamped) applied to the other two edges of the plate shift up the instability region and resonance curves in the parameters plane and, from a physical point of view, the system becomes more stable. In addition to using numerical simulations of the plate midpoint displacement, Floquet theory is also employed to validate the HAM results. Finally, the results of this study, in a particular case, are compared and validated with the results of other works.